Question

x = sec theta + tan theta then x plus one upon X equals to what

Answer 1

X=secA+tanA
X=(1+sinA)/cosA
1/X==cosA/(1+sinA)
X+1/X=(1+sinA)/cosA +cosA/(1+sinA)
=(1+sinA)^2+cos^2A/(1+sinA)cosA
=1+sin^2A+2sinA+cos^2A/(1+sinA)cosA
2+2sinA/(1+sinA)cosA
2(1+sinA)/(1+sinA)cosA
2/cosA
2secA

Answer 2

Given,

x = secФ + tanФ

To find,

x + 1/x

Solution,

x = secФ + tanФ

x = (1 + sinФ) / cosФ

1/x = cosФ / (1 + sinФ)

x + 1/x = (1+sinФ)/cosФ + cosФ/(1+sinФ)

          = (1+sinФ)² + cos²Ф/(1+sinФ)cosФ

          = 1 + sin²Ф + 2sinФ + cos²Ф/(1 + sinФ)cosФ

          = 2 + 2sinФ/(1+sinФ)cosФ

          = 2(1 + sinФ) / (1+sinФ) cosФ

          = 2/cosФ

          = 2secФ

Hence, x + 1/x is equal to 2secФ.